TL;DR Pop music isn't really ionian or aeolian, but does have a limited set of notes it uses. There are a few reasons why.
I won't disagree that modern pop music certainly has a specific tonal palette, but I think the analysis that it's based off of the ionian and aeolian mode is a little off. Most pop music isn't that modal at all, it's more chord based and "scales" change all the time based on context.
In cookie cutter minor pop music major 6ths and 7ths are common1 (even more so in classical music.) (not aeolian)
In major pop music, flat 7ths are found aaaaall the time, often in the same song as major 7ths2. A minor 4 chord in a major key isn't super uncommon either3.
There absolutely is a common theme though. In "radio pop" the third doesn't change (stays major or minor depending on the song). The 6th and the 7th can be whatever you want. The second is never flat. The flat 5 isn't used.
So a pop song in C can contain:
C, D, E, F, G, Ab & A, Bb & B (ionian plus Bb and Ab)
C, D, Eb, F, G, Ab & A, Bb & B (aeolian plus A and B)
I'm giving no reference with this, it's just what I've noticed over the years from living a radio filled world with musically trained ears, I imagine that everyone here will agree with this analysis (I hope).
Chordally, it will be based around triads (major and minor chords). You might see a dominant 7th on the 5 chord 4, or minor 7ths on the 1, 4 and 5 chord5, but only where these are "non controversial" i.e. they don't add in a note that wasn't in the above scale anyway and therefore do not change the harmonic "flavour". You are not going to have diminished chords, minor sixth chords, half diminished chords, major 7th chords etc. etc. etc.
So your question phrased more accurately might be:
"Why are the both 6th and both 7ths heard in pop music, but not both 2nds or the 4ths. Or really the 3rds (one or the other per song). And why are minor 7th chords heard, but never major 7th chords, never minor 6th chords or their inversions?"
The answer to that is, I'm not sure, but I have some ideas.
first of all, the harmonic series. This explains why no one is playing music based on tritone chords, but doesn't explain why pop music and, say, indian classical music, sound different.
If you'd asked me a year ago I'd have said because pop music is heavily influenced by the guitar, and mainly uses chords that are easy to play on a guitar, it's just what naturally comes out when people write by ear with open guitar chords. But now I'm getting into latin music, which is equally "just written by ear by people with guitars" music, I realise that it follows completely different conventions. In latin music the minor sixth is king. Many common harmonic tricks from pop music are rare or absent, but other simple latin tricks (like a minor 1 chord changing to a major 1 chord to lead to the minor 4 chord.) would NEVER happen in pop music. There is nothing more "complex" one or the other, it's just the way it is. I'll be damned if I know why.
Other people might answer in terms of theory from the classical tradition. But many things that are common in pop music have no precedent in the classical tradition, such as a chord based on the flat 7 of the key, or using a minor 7ths as a tonic chord.
I would say, a bit of all of the above is true, but also, fashion and convention. People write music that sounds like the music they are hearing. Pop music does get a lot from western classical music, and also from folk music, and (to a much lesser extent than in the past) blues music. Conventions stick around because of habit. Innovations happen sometimes, a popular song doing something that sounds good and is different might become a part of the popular idiom (a more trivial example of this which isn't harmonically different to previous music but demonstrates the effect of musical idea propagation is "the millenial woop"). The beatles had a few innovative tonal tricks that are now pretty mainsteam for example. Things go out of fashion too. For example, you hear a lot less seventh chords now than in, say, 70s music. On the other hand you have a lot more leading tones (sharp 7) in minor songs than in the 70s i.e. minor songs are less aeolian than they were, people seem to be reborrowing from classical music in that sense, (probably because more of the actual songwriters of songs on the radio are people who have had at least some formal music education, which involves theory based in the classical tradition).
in case it's easier for you here's all those intervals in C
1 A natural and B natural in C minor
2 B flat in C major
3 an F minor chord in C major
4 G B D F
5 C Eb G Bb F Ab C Eb and G Bb D F
6 Bb Chord in C.